Abstract:
The goal here is to classify an infinite class of rotationally-invariant equilibria of a weighted Dirichlet energy, subject to an incompressibility constraint on the solution. Specifically we consider as candidate solutions “whirl” maps, which are uniquely characterised by a oneparameter family of curves over the compact Lie group SO(n). A study of irrotational vector fields leads to a striking difference in the solution of this problem depending on whether the underlying spatial dimension is odd or even.
Biography:
George Morrison is a Postdoctoral Fellow at NYU Shanghai. Prior to joining NYU Shanghai in January 2019, George studied at the University of Sussex as an undergraduate and postgraduate, culminating in the award of a Ph.D. in the fall of 2018. His main research interests are calculus of variations and partial differential equations.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai